A Study on Fixed-Point Techniques under the α-ϝ-Convex Contraction with an Application

Abstract

In this paper, we consider several classes of mappings related to the class of α-ϝ-contraction mappings by introducing a convexity condition and establish some fixed-point theorems for such mappings in complete metric spaces. The present result extends and generalizes the well-known results of Singh, Khan, and Kang (Mathematics, 2018, 6(6), 105), Istra˘tescu (Liberta Math., 1981, 1, 151–163), and many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results. Finally, we derive the existence and uniqueness of a solution to an integral equation to support our main result and give a numerical example to validate the application of our obtained results.

Editorial: Overview and Some New Directions

“…The research of Gunasekaran Nallaselli, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Ozgur Ege, Dania Santina and Nabil Mlaiki in reference [3] involves a study on fixed-point techniques under the α--convex contraction with an application. In this paper, they consider several classes of mappings related to the class of α-Σ-contraction mappings by introducing a convexity condition and establish some fixed-point theorems for such mappings in complete metric spaces.…”

New Fixed Point Theorems for θ − ω − Contraction on λ , μ

“…Fixed point theory is an important and fascinating subject, and it provides essential tools for solving problems arising in various branches of mathematical analysis, see [1][2][3][4][5]. Fixed point theory guarantees the uniqueness and existence of the solution of integral and differential equations.…”